Rosenfeld (1965) Newton and the Law of Gravitation

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Newton and ae L aw of Gravitation

L ROSENFELD

T h e r e h a s b e e n r e ce n t l y a w el c o m e r e v i v a l of N e w t o n i a n s tu d ie s. T h e R o y a lSoc ie ty has a t long las t mad e a s ta r t w i th th e pub l ica t ion of the cor responden ce 1.

Va r ious s ch o l ar s h av e b r o ug h t t o li gh .t m u ch i n t e r e s ti ng new ev idence f rom thetoo long neg lec ted NEWTON ma nus cr ip t s 2. Fo r the f i r s t t ime a th orou gh andcom pe ten t s t ud y 3 h a s b e e n m a de o f a si de o f h i s a c t i v i t y w h ich had h i t he r t oremained obscure : h i s h i s to r ica l researches , co loured by theo log ica l cons idera -t i ons , t o w h ic h he h i mse l f a t t a c h ed g r ea t impor t ance . B y p i ec ing t oge the r a llth i s new e v idence .with long know n, bu t l i t t l e un ders to od fac t s, one a r r ives , as Iin ten d to show, a t a v iew of NEWTON'S perso na l i ty ra the r d i ffe ren t f rom thet r ad i t i ona l o n e. Th e . l a t t e r i s v e r y mu ch i n f luenced by he ro w or sh ip 4, bu t i tdoes no t he lp t o r e a c t t o t h i s - - a s r e cen t b iog raphe r s a r e i nc li ned to do - - by he rodebunk ing . N EW TO N'S p e r s o n a l i t y i s no t e a sy t o und e r s t and : s ec r e t ive and

susp i c ious a s he wa s , o ne ha s t o c a t ch h im , so t o speak , i n ungua rded momen t sto ge t a g l im pse o f h i s t h o u gh t s and o f h i s pa s sions. To r eco ns t ruc t a cohe ren tpo r t r a i t f r om the s c r a ps o f ev id en ce g l eaned f rom h i s pape r s , h i s l e t t e r s and h i sac t i ons is a h a r d de t e c t i ve w o r k , bu t a r ewa rd ing one .

In 'NEwTO I ~ 'S t h ou g h t , t h e p r ob l em o f unde r s t and ing t he cons t ruc t i on o ft he un ive rs e , w h i ch l e d h i m t o t h e d i s cove ry o f t he l aw o f g r av i t a t i on , doub t l e s soccup i ed a c en t r a l po s i t i on , a l t h ough i t was by no means t he p rob l em wh ich her ega rd ed a s t h e m o s t d e c is i v e and t o wh ich he devo t ed l t he g r ea t e s t e ffo rt .I ndeed , i t i s s t r a ng e h ow c a s ua l l y he dea l t w i th i t b e fo r e HALLEY wi th m uchd i f f i cu l ty m a n a g e d t o w r i n g ou t o f h im the w ork wh ich we e s t eem h is g rea t e s t .

The re i s c e r t a i n l y so me t h i ng i n t h i s a t t i t u de wh ich deman ds exp l ana t i on . Thec i r cums t an c es o f t h e d i s c ove r y o f t he l aw o f g r av i t a t i on p r e sen t a f u r t he r puzz l i ngfea tu r e , wh i c h ea r l y a t t r a c t e d t h e a t t en t i o n o f h i s t o r ian s : a f t e r he had t he

1 Three vo lumes have sof r appe ared, cov ering the period up to t69 4 (refs. [1--3 ]).In the fol lowing, documents publ ished in theCorrespondence will }be qu oted by theirnumber, fol lowed, for greater convenience, by the reference t@the volume; thusno. 288 [2] mea ns the letter no. 288, p ublished in volu me 2. ~

2 Espe cially A. R. HALL [4, 53, J .W . HERIgEL[6--93 A. KOYR~ [103 D.T.Wm~ESIDE [29 303.

3 See MANUEL'S bo ok [11] and my rev iew of i t [123.4 This is very conspicuou s in BREWST~R'S bio gra phy[133 but in fa i rness to this

author, i t should be st ressed tha t he is rem ark abl y accurate and rel iable in his accountof the facts. Much worse is the case of THOMSON& TAIT, whose judge men t of th eformulat ion of the fundamental laws of mechanics in thePrincipia (ref. [14]chap ter I I , especially § 263, 264) is ve ry uncri t ical and v i t ia ted by a qui te unhis tor icalinterpre tat ion of act i o as mechanical , work.

Arch. Hist . Exact Sci. Vol. 2 25





NEWTON and the La w of Gr av itat ion 367

upon b y su ch a f o rce a b od y w ou ld dev i a t e f r om i t s i ne r ti a l mo t ion and becons t ra ined to revo lv e in a c losed orb i t in a s imi la r way as a con ica l pen dul um or

a bo dy a t t~ . ched to a r o t a t i ng wh ee l ; and i n t he l a t t e r t y pes o f mo t ion , he wasaware o f t h e i n t e r p l ay o f t h e fo r c e de f l e c t i ng t he body f rom i t s i ne r t i a l mo t ionand an end ea v o u r o f r e c e s s o r c en t r i f uga l f o rce , t he two ba l anc ing each o the ra long t he a c t u a l p a t h o f the b od y. Assuming , t hen , t ha t t he young s t uden t (whoseex t rao rd i na ry g i f t s had a l re ady imp ressed h i s t eac her ISAAC BARROWx°) startedf rom a s im i la r c on c ep t i o n o f t he n a tu r e o f t he m oon ' s mo t ion , w e see t ha t t he ma inp rob l em fo r h i m w a s t o e v a lu a t e t he cen t r i f uga l a cce le r a t ion o f t h i s bod y on i t sve ry ne a r l y c i r c u l a r o r b i t : f o r i t wou ld g ive h im d i r ec t l y t he acce l e r a t i on due t othe a t t r a c t i o n f rom th e e a r t h . We sha l l t he r e fo r e have t o enqu i r e how NEWTONcame to kno w t he e xp r e s s io n fo r t he cen t r i f uga l a cce l e r a t i on

A = (~ -~ ) R (1)

(or some equ iva len t one) in t e rm s of the pe r iod of revo lu t io n T and the rad ius Rof the orb i t .

The nex t s t ep i s t o a s su m e f o r t he a t t r a c t i on t he i nve r se squa re l aw : one t henf inds it s v a l ue a t t he s u r fac e o f t he ea r t h f r om the p ropo r t i on a :A=R2:r ~ ,where the smal l l e t t e r s re fe r to the ea r th , the c .ap ita ls to the m oo n; and oneexp ec ts th i s ac ce le ra t ion a to be the sa me as tha t o f a f ree ly fa l ling body . Thiss t ep w as n o t d i f fi c u l t t o ' m ak e f o r NEWTON i f he kne w the fo rmu la ( t ): f o r t he

inve r se squa r e l aw i s a n i m m e d i a t e consequence o f i t, when i t i s comb ined w i thKEPLER 'S t h i r d l a w o f p l a n e t a r y mo t io n T o¢ R ( We ha~e d i r ec t ev idence n t ha tNEWTON did draw th i s con c lus ion a t the t im e; indeed , as we sha ll see, i t was a l sod rawn a t a l a t e r d a t e , i n d ep e n de n t l y, by HOOKE and o the rvirtuosi. I t n eededNEWTON'S c r i t i ca l acume n, h owev er, to be aw are of i t s poss ib le l imi ta t ions : bu tof th i s l a te r. Fo r a num er ica l e s t im ate o f the acce le rat ion , a on the bas i s o f thepreced ing a rgum ent , NEWTON needed , bes ides the w el l -known va lues o f the m oo n ' spe r i od o f r ev o l u t i on T a n d t h e r a t i oR : r be tween t he r ad iu s o f t he m oon ' s o rb i tand t he ea r t h ' s r a d iu s , a l s o t he abs o lu t e va lue o f t he l a t t e r : i n f a c t, t h e va luefound fo r a d e pe n ds l i n e a r l y o n t h a t ado p t ed fo r t he ea r t h ' s r ad iu s . H e re we mee tt he ques t i o n a l l u d e d t o a b ov e : w h ich va lue d id NEWTON use ? Le t u s now lookin to h i s ea r ly inves t iga t ions of the law of cen t r i fuga l fo rce ; these wi l l a l so sugges tus a p laus ib le answer to the las t ques t ion .

The ana l y s i s o f c i r cu la r mo t io n i n t e rms o f a c en t ri f uga l t ende ncy goes backto GALILEI. In the secon d d ay of hisDialogo E19~o f t 632 , devo t ed t o t he . examina -t i on o f t he o b j e c t i o n s ra i s ed a ga in s t t he e a r t h ' s m o t ion , t he ques t i on comes upwhe the r a ll b od i e s, h o w e v e r h e av y, wou ld no t be hu r l ed i n to space from the

10 To be quite precise, BARROW was not too pleased with NEWTON whe n he exa m-ined him in geom etry in 1664 BREWSTER[131, vol. 1, p. 24~;. bu t he mu st hav e soon

formed a bet ter opinion of him, s ince NEWTON'S discovery of the meth od of fluxionsis recorded as ear ly as May 20, 1665 ibid. p. 25). ; the first written expressions ofBARROW'S est ee m for NEWTON da te fr om 1669 (letters nos. 5- -7 [•]). Mo re evid enc e o n

.NEWTON'S ear ly intel lectual developm ent , as wel l as indirect in formation on theprecise natu re of his relations w ith BARROW in his st ude nt years, is found in a well-doc um ente d article by D. T. WHITESlDE [29].

xl Letter no. 288 [2].25*



368' L. R O S E N F E L :

sur face of the moving ear th as a s tone i s hur led f rom a s l ing . Wi th re f ined i ronyGALILEI cont r ives to pu t th e re fu ta t io n in the ve ry m ou th o f ,S impl ic io , who

is dr iven b y c lever ques t ion ing to recognize tha t a bod y on the ear th i s no t Carr ied~ away a long a tang ent to the sur face wi th th e fu l l ve loc i ty of the ear th ' s mot ion ,bu t on ly li f ted a long the r ad ius t owards t he t angen t a t t he im med ia t e ly p reced ingposi t ion. GALILEI is no t able, how ever, to give a q ua nti tat i ve analysis of theeffec t : he jus t has the cor rec t fee l ing tha t i t mus t be m uch smal le r tha n theforce of grav i ty.

HUYGENS [20] was the f i rs t to br in g GALILEI'S arg um ent to com plet ion.This work da tes f rom t659 , when HUYGENS, who was t hen th i r t y, had r eachedthe ma tu r i t y o f h is gen ius. H i s t r ea tm en t o f t he p rob lem i s mas t e r ly be t t e rin fac t than m an y a mode rn tex tbo ok expos i t ion . GALILEI'S poin t i s made m ost

P

/\

\ /

Fig t Analys is of c imular mot ion by HOYGE~S

/ \

\z1

Fig 2 Analys is of c i rcu larmotion y NEWTOr¢

e l egan t ly by cons ide r ing the m o t ion f rom the po in t o f v i ew o f an obse rve r pa r t i-c ipa ting in ' t he ro t a t i on : fo r such an obse rve r t he dev ia t i on f rom the i ne r t i ~mot ion du r ing a ve ry sho r t t ime in t e rva l may indeed be app rox ima ted by a~mar ion towards the cent re . This i s shown by a minute k inemat ica l ana lys is ,exh~ibiting HUYGENS- sk il l i n deal ing wi th p rob lems o f con t inu i ty by the me tho dsof the anc ien t geometers . I f Fig. t) the a rc P B i s ve ry smal l, the rad ia l d i s tanceA B i s eas i ly seen to be ap pro xim ate ly equal to th e squ are of the a rc P B, d iv ided

by the d iameter, and thu s prop or t iona l to the square of the t ime. This is p rec ise lythe_ same law as t ha t of the free fall , so tha t the cent r i fug al accelerat io n is im-med ia t e ly s een to be g iven by the p roduc t o f t he r ad ius and the squa re o f t heangular veloc iCy, as expr essed by the form ula (1).

How ever , HUYGENS did no t pub lish th e law of centr i fu gal ~tccelerat ion unt i lt 673 , when i t appea red a s an append ix t o t heHorologium oscillatorium [21]NEWTON knew i t in 1665 because he ha d d iscovered i t the yea r before (a t theAge o f twen ty - two) by h i s own exer t ions . Ea r l y pape r s r ecen t ly b rough to l i gh td isc lose the devious pa th by which he a r r ived a t the goa l : there i s no t race hereof the scholar ly eleganc,e of the Du tch phy sicis t ; NEWTON'S app roa ch appe arsby con t r a s t cu r iously s imp le -minded and uncou th , I t bea r s the ma rk o f h i s t e ache rBARROW, whose d idac t ic works h era ld th e f ina l brea k w i th th e anc ien t geom etr ica lt r ad i t i on in f avour o f t he mode rn ana ly t i ca l me thods ; a t endency s t i l l moreevid ent , of course, in NEWTON'S f i rs t a t te mp ts , f ro m the same p eriod, at a syste-mat ic represen ta t ion o f geom etr ica l ly def ined func t ions by inf in i te se r ies.



NEWTON and the Law of Gravitation 369

In his ana lysi s of circular motio n 1~, NEWTON discusses the case of a globemoving along a great circle inside a hollow sphere: the inertial motion of the

globe is continuously impeded by the spherical surface, which experiences apressure from the globe; this centrifugal pressure is measured by the change ofmo men tum corresponding to the deviation of the globe's inertial motion. NEWTONfirst obtains a lower limit for the effect by observing that in a half-turn theVelocity of the globe is just reversed : its total end eav our from the ce nter ina half-turn is thus at least twice its momentum. A better estimate follows fromthe case (Fig. 2) in which the globe, with th e same velo city as in the actua lcircular mo ti on , just bounces four times in a complete tu rn against the sphere,thus describing the four sides of an inscribed square: this gives the proportion

endeavour from centre at each reflexion side of inscribed squaremomentum radius of sphere '

and further

tota l emdeavour from centre in one turn _ perimeter of trajectorymom en tum radius of sphere

It is easily seen that this argument holds for any regular inscribed polygon aswell as for the square, so that by a passage to the limit familiar from ARCHIMEDESNEWTON could conclude tha t in the a ctua l circu lar motion, .the tot al endeavourfrom the centre in one revolution is to the momentum as the circumference tothe radius: this gave him the value ~ instead of the lower limit 2 for the sameratio for a half revolution. Also, in view of the perfect uniformity of the process,we may say that the total end eavour from the centre during the time tha t thebody describes an arc equal to the radius is just equal to the momentum. Howcan one pas s from this inte gral law to an expression for the instantaneousforce ? For NEWTON'S powerful i ntuiti on, the cont inuous cha nge of direction ofthe centrifugal force is no embarrassment: its effect must be the same as if themotion, in stead of being constrain ed to the spherical surface, were allowed t oproceed on a p lane: but then we have the p roblem solved b y GALILEI of theeffect of a constant force, like gravity, acting perpendicularly to the trajectoryof a uniformly moving body. The total ~ffect of the constant acceleration Aduring a time t is to produce a velocity A t: now, we have found that if the timeis R / V R denoting th e radius of the sphere, V the velocity of the circular motion),the acquired velocit y is just V. Therefore, A -- V2/R, an expression for the centri-fugal acceleration equivalent to the formula (I) above.

It is not sure what incited NEWTON to this high ly original stud y of the circularmot ion: it ma y h ave been, as cert ain of his notes suggest 13, a read ing of DES-CARTES Principia philosophiae. However, while the latter's influence on HUY-GENS as well as NEWTON rema ined pa ramoun t for the ir general conc eptio n ofthe transmission of force by contact, Cartesian ~tynamics was too crilde and

erroneous to be in the taste of such acute and independent minds. For both ofthem, the true source of inspiration in their dynamical thinking was GALILEI.

12 My accoun t is based on the documents published by HERIVEL [61, but differsin some particulars from his own inte rpreta tion of them [6, 81 .

13 See on this point HERIVEL'S [C, 8~ remarks. An ear ly essay by NEVCTON pertain-ing to DESCARTES' Principia philosophiae is published in ref. [5], p. 89--156.



370 L ROSENF ELD:

Othe r ma nus cr ip t s 1 . f rom th e same t im e g ive ev idence of NEWTON'S read in g theDialogo an Eng l i sh t rans la t ion of which by SALUSBURY had been a va i lab le s incet661 . In one of these 15, one f inds a ne w der iv a t ion of the law of cen t r i fuga lforce very s imi la r to HUYGENS ;b u t i t w a s c le a r ly a n a f t e r th o u g h t . A rg u m e n t sbased on th e pr inc ip le o f re la t iv i ty, o f which GALILEI and HUYGENS ma de suchbr i l l i an t use , n eve r app ea led t 9 NEWTON: wh at he too k f rom GALILEI wasr a the r, a s e xe mp l i fi e d b y h i s a n a l y s i s o f c i r cu la r mo t ion , t he more dy na mic a la spec t o f t h e l aw o f i n e r ti a , t h e i dea o f i nves t i ga t i ng t he fo rce s de t e rmin ing t hem o t i o n o f b o d i e s b y t h e c h a n g e s o f m o m e n t a t h e y p r o d u c e .

One has a l so re t r i ev ed 16, and HERIVEL has ve ry sk i l fu l ly dec iphered , thesc r ap o f pap e r o n wh ic h N EW TON jo t t ed dow n the numer i ca l com pu ta t i o ns l e ad -ing t o t he qu an t i t a t i ve e s t ima t e s wh ich we re s t i l l wan t i ng , a s I po in t ed ou t

above , in GALILEI'S a rgu men t . We see NEWTON app ly in g h i s n ewly acqui redknowledge of the law of cen t r i fuga l fo rce to ca lcu la te th i s fo rce a t the sur faceo f t he ea r t h a nd co mp a r e i t w i t h t he fo r ce o f g r av i t y. Th i s p r ecious docume n tanswers ra the r def in i te ly th e ques t ion which v a lue NEWTON did ado pt . fo r theea r t h ' s r ad iu s i n h i s f am ou s me d i t a t i on unde r t he app l e t r ee . A l e a rned pap e rhas been wr i t t e n o n t h i s q ue s t i on by 'CAIORI [15]: he pa in s t ak ing ly co l l e c t eda l l t he da t a he co u l d f i nd i n t he books on nav iga t i on o f t he t ime and Wen t onto Specula te to wh at e x te n t NEWTON could be exp ec te d to ha ve co gnisance oft h i s l o r e . He o ve r lo ok ed , ho w ev e r, one i t em , t he one t ha t was pe rhaps t he mos tobv ious , an d t h a t a t a n y r a t e h a s now tu rned ou t t o g ive a deci s ive c lue , to w i t

GALiLEI SDialogo. I n t he c a l cu l a ti on j u s t men t i oned , NEWTON na tu r a l l y enoughbo r rows f r om t he bo o k h e wa s s t u dy ing t he va lue he needed : i t i s unmis t akab lyquo t ed a s 35 00 I t a l i a n m i le s . Ad m i t t ed ly, we canno t be abso lu t e ly su re t h a tNEWTON use d t h e s a me v a l u e i n t he o the r c a l cu la t i on , bu t t he p rox imi t y o fda t e s an d c i r c u m s t a n ce s m a k es i t ove rwhe lming ly p robab l e . Now , t h is va lue i sve ry rough indeed , abo ut 16 too smal l : obvious ly, G,ALILEI rega rds i t jus t asa r ound nu m b e r e a s y to m e m o r i z e and su ffi c i en t fo r r ap id e s t ima t e s . I t i s no t e -wo r thy t ha t t h e v a l ue q u o t ed b y GALILEI fo r t he acce l e ra t i on o f g r av i t y i s mu chworse : i t i s ab ou t ha l f the t ru e va lue . This NEWTON f inds unac cepta b le , an d h e .de t e rmines h ims e l f a mo r e c o r r ec t va lue by means o f expe r imen t s on t he t imeso f o sc i l l a t i on o f s i m p l e a nd co n i ca l pendu lums ; by i t s e l f ano the r r emarkab l each i evemen t . H e i s ap pa re n t l y u nconce rned , howeve r, abou t t ak ing ove r GALl -EEl'S va lue of the e a r th ' s rad ius .

I f he u s ed th i s v a l ue , h e fou nd a d i s c r epancy o f t he o rde r o f t 6 be tweenthe ca lcu la ted a t t ra c t io n a t th e sur face of the ea r th and tl~e force of g ra v i ty 1~.

l , These are the ma nuscr ipts f i rs t publ ished by HA LL [4] an d reproduced as docu-men ts no: 1 t 7 [1] and 347 [3]. A comparison of the l atte r wit hSALUSBURY S ranslat ionof GALILEI'SDialogo was p erformed by the la te Prof. H . W.TURNBULL,first editorof the Correspondenceand is repo rted b y HERIVEL[7] ; i t reve als convin cing analogies.

15 T h is is no. t t7 [1].1~ This~is no. 347 [3~, which is inter preted by the edito r of the third vol um e of the

Correspondence Dr. J. F. SCOTT, bu t more fully by HERIVEL[7].1~ This is in agree me nt w ith the figures quoted by BREWSTER[13] VO1. , p. 26,

in his acco unt of NEWTON'S work at V¢oolsthorpe: accord ing toBREWSTER,he foundfor the def lexion in one second d~le to th e at t ract io n at the surface of the ear th avalue of 13.9 feet, whereas that due to gravify is t6.1 feet.



NEWTON and the La w of Gr av itat ion 3 71

W ha t d id he t h in k o f su ch a r e s u l t ? We hav e t he t e s t imon ie s o f PEMBERTON andWHISTON who kne w NEWTON wel l in l a te r yearsTM. T h e y g i v e t h e i m p r e s s i o n

t h a t h e r e g a r d e d t h e o u t c o m e a s c o n d e m n i n g t h e i d e a h e w a n t e d t o t e s t ; t h e ymen t ion t he w ro n g va lu e o f t h e ea r t h ' s r ad iu s a s the cause o f t he f a il u re , bu tth i s i s a re t ro spe c t iv e co ns idera t io n which th row s no l igh t on NEWTON'S poss ib lemo t ive fo r b e i ng s o ca su a l ab ou t t h i s co ns t a n t . On t he o th e r hand , NEWTONhimse l f , in a m em or an du m 19 of 17 t4 , wr i tes tha t he found h i s ca lcu la t ions ans we rp re t t y nea r l y , w h i c h w ou ld s u g ges t t ha t h e was no t so d i s s at i s fi ed w i th t her e su l t . A f t e r a l l, n one o f t h e co m men ta to r s , p rone t o d r ama t i z a t i on , ha s eve rr a i sed t he s i m p l e -m in de d que s t i o n : how ne a r l y d id NEWTON ac tua l l y expec ttha t the two acce le ra t ions w ould agree ? WHISTON gives a fu r th er p iece of in for-ma t i on 20 w h i ch ap pe a r s h i gh ly r e l evan t i n t h i s r e spec t : he s t a t e s t ha t NEWTON

inc l ined to the conc lus ion tha t bes ides g rav i ta t ion , some o ther cause , such as aCa r t e s ian vo r t e x , m i g h t c o n t r i b u t e t o de t e rmine t he mo on ' s mo t ion . Th i s is no tas unplaus ih le as i t might seem: more d i rec t ev idence of the in f luence of Car tes iancosmo logy on N E WTON'S e a r l y v i ews o f t he moo n ' s m o t ion ha s i ndeed r ecen t l ybeen b ro ug h t t o l i g h t 21. O n ly b y pu r su ing t he s t o ry can we hope t o f i nd fu r t he rc lues . So fa r, howe ver, i t wi l l be c lea r to eve ry sc ien t i s t th a t NEWTON a t th i ss t age had op en ed up f o r h i mse l f a n exc i t i ng p ro spec t , bu t had no th ing f i t t o bepubl i shed .

Du r ing the d ecade fo l lowing h is re tu rn to C ambr idge , in 1667, w e f ind NEWTON

engrossed i n h i s op t i c a l i nv e s ti g a t i ons , a s we ll a s bus i l y engaged i n ma them a t i ca lco r r e sponde n c e w i t h C OL LIN S. T h e re i s impo r t an t ev i den ce f rom the se yea r s ,howeve r, t h a t f a r f r o m l o si ng si g h t o f t he p rob l em o f g r av i t a t i on , he deve lopedabou t t he n a t u r e o f t h i s f o rce sp e cu l a t i ons o f ex t r a o rd i na ry dep th and bo ldness .The f i r s t p iece of ev idence , a l tho ugh som ew hat ind i rec t , i s s ign i f ican t enough tobe quo t ed . W h e n i n t 6 7 3 he r ec e i ved fromH uYG ENS a copy of t heHorologiumoscillatorium, NEWTON did no t fa il , in h i s message of thanks , to in t im ate in acove r t way ( a s wa s t he cu s to m among t hevirtuosi t h a t he a l so had l ong knowna ll abou t t h e ce n t r i f u g a l f o r ce : t h i s he con t r i ved t o do b y g iv ing a s an ex amp leo f i t s u se fu l n e ss t he a p p l i c a t i o n h e h ad mad e o f i t t o t he compa r i son o f t he r e spec -

t i v e a t t r a c ti o n s e x e r t e d b y t h e e a r t h o n t h e m o o n a n d b y t h e s u n o n t h e e a r t h .Al lud ing mu ch la te r 22 to th i s message , NEWTON be l ieved th a t he ha d even me n-t i oned exp l i c i t l y i n it t h a t su ch a com pa r i son wou ld l e ad (i n connec t i on w i thKEPLER'S th i rd law) to the inv erse sq uare l aw for the a t t rac t ion ; in fac t , th i s i s

is See BREWSTER[131, VO1. 1, p. 290-'--292 an d CAJORI[161.19 Quoted e.g. b y CAJORI [151, p. t60.2o Th is is q uo te d b y ]~RE'~STER[13~, VO1. t, p. 290.21 See an i mp or tan t p ap er by D. T. WHITESlDE[305, who analyses ear ly as t ronomi-

cal manusc r ipts of NEWTON and annota t ions found in books he read a nd t races theirre la t ion to the contemporary background , o f which he makes an ex tens ive s tudy.I t is notewo rthy t ha t NEWTOZ¢ showed as l i t t le appreciat ion as the pract ical as t ron-om ers of his t im e for the significance of KEPLER'S two first laws. In partic ular, h eignored the second law ( the law of areas) unt i l he found t ha t i t was a consequence ofthe inverse square law of a t t ract ion.

22 See t he beg inn ing of lett er no. t 16 -[1~ toOLDENBURG with the edi tors ' comment .Ne wto n refers to this le tt er in his correspond ence with HALLEY in t686 (nos. 288and 291 [21).



372 L . ROSENFELD:

not in th e le t te r, as he soon could ascer ta in when he foun d a co py of i t ; th e omis-s ion surpr i sed h im : obvious ly, he rem emb ered h is or ig ina l in ten t io n of comm uni-

ca t ing to HUYGENS a fu l le r accou nt of h i so ld inves t iga tions . Th is shows a t anyra t e t ha t he had no t g iven them up .An othe r cur ious fac t emerges f rom an ex change of le t te rs 28 he ha d in Ja nu ar y

1680/1 with THOMASBURNET a t the occas ion of the publ ica t ion of the la t te r ' sb o o k Tdluris theoria sacra which represented one of the ear l ies t a t tempts a t asc ien t if ic the ory of the form at ion of the ear th . BURNET havin g asked , amo ngothe r th ings , for NEWTON'S opin ion abo ut the shap e of the ear th , the l a t te r r e -p l ies tha t to the bes t o f h i s judgem ent , based on the ana logy wi th th6 o th er p la -ne ts , i t is spher ica l ; he in t ima tes tha t th e e ffec t of ro ta t ion m ust b e negl ig ib le .Bes ides , he can not te l l wh at to m ake of the ev idence Of geodet ic measu reme nts ,

no t know ing how exac t ly t hose measu re s were made o r the l a t i tudes o f p l acest aken . Th i s s t a t emen t he lps u s a t l e a s t t o unde r s t and why he d id no t showeven a t th ig la te r d a te more eagerness to loo k for the b es t ava i lab le v a lue of theear th ' s rad ius .

The d iscuss ion wi th BURNET is in te re s t ing f rom another, more genera l , po in tof v iew. I t giv s us a gl impse of. an aspect of NEWTON'S thin kin g 'so unc ong enialt o u s t ha t i t ha s been mos t ly neg lec ted o r mi sunde r s tood by b iog raphe r s : I m eanhis a t t i tu de to theologica l problems, in the present instance, while BURNETdismisses the f i r s t account of c rea t ion in Genesis as pu r e ly i dea l , :w i thou tre la t ion to phy s ica l rea l i ty , NEWTON defends i t, m os t ingenious ly, as a con-

s i st en t de sc r ip t ion o f phys i ca l phenomena a s t hey. wou ld h a v e appea red to ahu ma n obse rve r i f any such cou ld have wi tnes sed them f rom a t e r r e s t r i a l van t ag epo in t . As t o t he phenom ena themse lves , he imag ines t he g radua l fo rma t ion o f t hesun a nd p lane ts as loca l condensa t ions Of the pr im eval chaos , perhaps b y an en-t i re ly na tur a l cause, such as the ac t ion of grav i ta t ion . The len gth of the successived a y s he conce ives as gradual ly decreasing as the ear th acqui res i t s p resents ta te of ro ta t ion : bu t here he a l lows for an immedia te d iv ine in te rvent ion , es t i -

• ma t ing na tu ra l causes in su ffi c ien t t o p r odu ce such a ro t a t i ng mo t ion . T h i s mix -tu re o f r a ti ona l i sm and theo logy i s ha rd fo r u s t o app rec i a t e ; b u t I hope to showin the las t par t o f th i s essay tha t i t can be made more access ib le by tak ing due

accoun t o f a l l c i r cums tances . A t any even t , i t wou ld be qu i t e wrong me thod i -cal ly to disreg ard a s ide Of NEWTON'S ac t iv i ty to which he him self a t tac he d per-haps more impo r t ance t h an to h is s c ien ti f ic w o rk .

Of s t i l l g rea te r in te res t for our enqui ry i s another document which revea ls tous NEWTON the sc ien t is t engaged in cons idera t ions of a chara c ter qu i te d i ffe ren tf rom the pene t r a t i ng induc t ive enqu i ri e s in to t he l aws o f na tu re fo r wh ich h e iscom mo nly ce lebra ted : i t i s a long pape r z4, wr i t te n some t ime abo ut 1675, and inwhich NEWTON develops th e hyp othes is of a. un iversa l ae ther, as the agent bywhich no t o n ly t he va r ious fo rces ac t ing on m a t t e r a r e p ropaga ted , bu t even mus -cular m6t ion i s in i t ia ted by th e soul . Th ere a re severa l o ther man uscr ip ts zS,as wel l as mater ia l publ i shed in the form of que r ies a t the end of theOptickswhich ex t end and mod i fy t he v i ews con ta ined in t he pa pe r we a r e cons ide r ing ;

~a Le t t e r s nos . 244 246 247 [11 .L e t t e r n o . 1 4 6 [ 1] .

36 See especially ref. [6], pa rt II I.



•NEWTON and the Law of Gra vitatio n 373

bu t i t i s the la t te r tha t p lays a dec is ive par t in the course of events we are t ry ing toana lyse . I t was comm unica t ed toOLDENBURG, t he s ec re t a ry o f t he R oya l Soc i e ty,

on D ecem ber 7 , 1675, th e imm edia te occas ion be ing NEWTON'S con t rov ersy wi thHOOKE on the na tu re of l igh t. NEWTON had va in ly t r ied to avoid th i s co nt ro vers yby a rgu ing tha t h i s t heo ry o f co lou r s was i ndependen t o f any a s sumpt ion abou tthe phys ica l cons t i t u t i on o f t he r ay s ca r ry ing these co lou rs . Now, he wan ted toshow HOOKE tha t he had noth ing to learn f rom him on th is las t ques t ion e i ther,and tha t i ndeed he had though t more t ho rough ly abou t t he cons t i t u t i on o f t hetmive r se t han any o f t hose vir tuosi whose heads run much upon hypo theses .

The deeper mot iva t ion , of course , was to acquain t a t l eas t the fe l lows of theRoya l Soc i e ty w i th a g ran d concep t ion o f t he work ings o f t he un ive rse on pu re lymechanica l pr inc ip les , in the bes t Car tes ian sp i r i t .N E W T O N S a t t i t u d e a b o u t i t

i s cur ious ly ambiguous : he fee ls tha t i t i s no t ma tur e and i s accord in gly re luc tan tto comm i t h imse l f; bu t he c l ea r ly r ega rds i t as so fundam en ta l t h a t he is impa-t ien t to p resent i t to t he judg em ent of h i s peers . He does not le t OLDENBURGpub lish i t 2s, bu t he al lows i t t6 be reg ister ed ,i.e. cop ied in t he r eg i s t e r o f t heSociety, whic h is on ly accessible to : the fellows. NEWTON'S fondn ess for th esespecula t ions , which so sharp ly be l ie h is hypotheses non / ingo , is a chal lengeto the h is tor ian . I sha ll t ake i t up in a l i t t l e whi le , and hav e occas ion the n tos t ress aga in the in t im ate re la t ionship be twe en NEWTON'S sc ien ti f ic specula t ionsand h is theologica l ly c01oured metaphys ics .

Fo r t he m ome n t , l e t u s on ly r e t a in t he r ema rkab le i n t e rp re t a t i on o f t he fo rceof gra~ci ta t ion proposed by NEWT6N in the f ramework of h is ae ther hypothes is .In the pap er i t se lf , the re i s on ly a br ie f and not too c lea~: ind ica t ion of i t ; when,how ever, in t686, NEWTON has occasion, as w e shal l see, to refe r HALLEY to i t ,he adds some comm ent s wh ich g rea t ly c l a r ify t he i dea w i thou t mod i fy ing i t i nan y w ay ~ . The idea i s tha t a bo dy l ike the ear th , o r the sun , i s the sea t of a cyc licp roces s o f t r ans fo rm a t ion o f t he ae the r : a s t r eam o f ae the r f al ls con t inua l ly uponthe e ar th and perv ades a l l it s par t s , i t s de ns i ty increas ing 'as i t loses m om en tumin in t e r ac t ion wi th t he g ross ma t t e r o f t he ea r th ; t h is condensed ae the r wou ldthen co n t inua l ly e scape f r o m the e a r th t o fo rm the a tmosphe re an d fu r the r t od isperse in to the ae th erea l spaces where i t would resume i t s or ig ina l form,thus comple t ing the cyc le . I n mod e rn t e rms , a cons t an t i nw ard s t r eam o f Sae the r par t ic les per un i t t im e mo ving wi th rad ia l ve loc itY v, has a t a d i s tance Rf rom the cen t re , a dens i tyS/ 4~ R ~ v, increas ing in the inverse ra t io of the ve loc i ty.Now, such a s t ream wi l l -exer t on gross : m at t e r a pressu reS m v/4 ~ R 2d i r ec t edtowards th e cen t re and , so long as the ve l oc i ty does not change app rec iab ly,inverse ly propor t iona l to the square of the c l i s tance , jus t as i s requi red for thea t t ra c t io n of the sun on the p lane ts by KEPLER'S th i rd law. Thus we see tha t inh is bo ld specula t ions ab o ut the cons t i tu t ion of the mate r ia l wor ld , NEWTONthoug h t o f g rav i t a t i on a s a un ive r sa l fo rce hav ing a ll t he appea rance o f an a t t r a c -t ion obeying the inverse square law, a l though i t ac tua l ly proceeded f rom a con-t a c t i n t e r a c ti o n b e t w e e n a e t h e r a n d m a t t e r. A g a in w e u n d e r s t a n d w h y h e d i dnot pub l i sh h is ideas a t such an imm atu re s tage , a l tho ugh h is a llowing the m to be

26 NEWTON'S cau tio us dir ecti on s to OLDENBURGare foun d in h is lette rs nos. 147,t 51 (postsc ript), t53 [1].

2~ See the end of the let ter s 288 ands291 [2].



374 L. ROSENFELD

regis te red i s an ind ica t ion of how con f ident he was to be on the t rack of essen-t ia l t ru ths .

On th e o ther hand , as we hav e noted , he fu l ly uph eld the conclus ion of h is re -f lex ions in t he Woo l s tho rpe ga rden , bu t app a ren t ly d id no t t h in k i t wor th h is wh il eto t ry and improve the r e su l t , f o r example by r e so r t i ng to a be t t e r va lue o f t heear th ' s rad ius . I th ink th is behaviour i s no t so puzz l ing as i t looks . Sc ien t i s t s dono t r e l i sh t he s t r enuous work wh ich any de t a i l ed i nves t iga t ion demands ; t heyonly engage in such w ork und er compuls ion . NEWTON was no t d i ffe ren t in th i sr e spec t f rom the r an k and f i le o f h i s c r a f t. Now, i t so happ ened t ha t i n t 679 andthe fo l lowing yea r s t he m om en t o f compu l s ion arose f rom an ex t r ao rd ina rysuccess ion of casua l events , and l i t e ra l ly dro ve NEWTON to the com ple t ion ofh is grea t work .

In Dec emb er t679 Ho oE E, who h ad succeeded OLDENBURG as secre ta ry ofthe Roy al Socie ty, took over th e care of the sc ien ti f ic cor respondence , prev ious lyas sumed by a s econd sec re t a ry, He used the oppor tun i ty t o make ano the r e f fo r tto res tore h is personal re la t ions wi th N E W T O N which had been bad ly s t r a inedby the . l igh t con t rove r sy. A p rev ious a t t emp t , imm ed ia t e ly a f t e r t he d i spu te ,in t675/6, ha d b een re ceive d by NEWTON (who was HOOKE'S junio r by seven years)wi th haugh ty condescens ion~s , and the k ind man fared no be t te r th i s t ime(tan-taene an4mis caelestibus irae ). In inv i t ing 29 NEWTON to com mu nic ate to the So-c i e ty wh a t sha l l occu r t o you tha t i s ph i lo soph ica l , he made the d ip loma t i c

b lun der of so lic it ing a lso NEWTON'S objec t ions aga ins t any hypo thes is or op in-ion o f mine , and o f men t ion ing pa r t i cu l a r ly h is i deas abou t com poun d ing thece les t ia l mot ions of the p lane ts of a d i rec t mot io n b y ' the tange nt and ana t t ra c t iv e mo t ion toward s the cent ra l b od y . NEWTON excused h imsel f a° bythe p re t ex t , ou t r ageous ly improbab le , t ha t he had been l a t e ly so mu ch ou t o ftouch wi th ph i lo so phy a s t o be i gno ran t o f r ecen t p roduc t ions : t hus , he d idnot re me mb er hav ing ev er heard of HOOKE'S hypo thes is ab out ce les t ia l mot ions .

Never the less , NEWTON - - to swe eten h is answer, as he la te r wro te a l toHALLEY - - did inser t in i t a ph i losophica l communica t ion . He poin ted out tha ta p roo f o f t he . ea r th ' s ro t a t i on cou ld be ob t a ined by obse rv ing the dev ia t i on o f a

fa l l ing body f rom the ver t ica l towards the eas t . In the f igure (F ig . 3 ) i l lus t ra t ingthe a rgumen t , he p ro longed the p a th AD o f t he f a ll ing bod y to t he cen t r e C o f t heea r th a s a smoo th cu rveDEC. This rem ar k e l ic ited a pro mp t rep ly 32 f ro m HOOKE :i f . the b od y could proceed ins ide the ear th , he sa id , i t would not descr ibe such a• u rve a s Newton h ad ske t ched , bu t r a the r an e l li pse- li ke t r a j ec to ry a rou nd thecent re ( the curve A F G H on Fig . 4 ) br inging i t back to i t s s ta r t ing poin t , i f therewas no res i s tance to the mot ion; a l lowing for such res i s tance , the pa th would bea kind of spiral l ike•A I K L M N O P ul t imate ly reaching the cent re C. Moreover,t he dev ia t i on f rom the v e r t i ca l wou ld on ly be exac t ly t o t he ea s t a t t he eq ua to r ;i n ou r no r the rn l a t i t udes , howeve r, i t wou ld r a the r be t o t he sou th -eas t , and in

Lond on even r a the r m ore sou th t han ea s t .2~ This alludes to the oft, quo ted exchang e of lette rs nos. 152 and 154 [13.29 HOOKE'S le tte r to NEWTON no. 235 [2].80 NEWTON'S re p ly no . 23 6 [2].81 In his le tte r no. 288 [2].

• z L ett er no. 237 E2].



NEWTON an d the Law of Grav i ta t ion 375

Ve ry mu ch aga in s t h i s wish 33, NEWTON was thus fo rced to con t inu e th e co r re -s p o n d e n c e , a n d , w o r s e st il l, t o a d m i t t h a t h e h a d b e e n i n e r r o r i n th e s h a p e o f t h e

i n s id e p a r t o f t h e t r a j e c t o r y . H o w e v e r, h e d o e s n o t d e i g n t o c o m m e n t o n H OO K E Ss o l u t i o n , b u t p r o c e e d s t o d i s c u s s t h e s h a p e t h a t t h e t r a j e c t o r y w o u l d h a v e i fo n e a s s u m e d t h e f o r c e o f g r a v i t y t o b e c o n s t a n t o v e r t h e w h o l e in s i d e o f t h e e a r t h .To t h i s H o O K E r e t o r t s i n t h e n e x t l e t t e r 34, w h i c h e n d s t h e d e b a t e , t h a t h e h a d i nm i n d t h e c a s e i n w h i c h t h e a t t r a c t i o n i s a s s u m e d t o o b e y t h e i n v e r s e s q u a r e l a wd o w n t o t h e c e n t r e . T h e p r o b l e m o f g r a v i t a t i o n w a s o n e o n w h i c h H OO KE, i n th em i d s t o f h i s b u s y li fe , n e v e r c e a s e d t o m e d i t a t e i n h i s o w n a c u t e a n d i m a g i n a t i v ef as h io n 35 ; h e h a s a ls o s t a t e d q u i t e p l a i n l y ~ t h e m o t i v e f o r t h is s u s t a i n e d i n t e r e s t :

A

Pig. 3. Path of falling bodyprolonged to the centre of theearth ccording to NEWTON

LIED

Fig. 4. Pa th of gr vi t t ing body inside the earth accordingto HOOKE

t h e u t i l i t y o f a g o o d t h e o r y o f p l a n e t a r y m o t i o n s f o r s o l v i n g t h e g r e a t p r o b l e m o fn a v i g a t i o n , t o d e t e r m i n e t h e l o n g i t u d e o f a s h ip s p o s i ti o n . H e m u s t h a v e r e a li z e dt h a t t h e a t t r a c t i o n o f t h e s u n o n t h e p l a n e ts m u s t o b e y t h e in v e r se s q u a r e l a wa s s o o n a s h e l e a r n e d f r o m H UY GEN S . b o o k t h e l a w o f c e n t r i f u g a l f o r c e ; w e k n o wf r o m e n tr ie s i n hi s d i a r y t h a t h e r e a d t h e b o o k i n N o v e m b e r t 6 75 a n d a t o n c es t a r t e d t h i n k i n g a b o u t t h e m o t i o n o f t h e p l an e t s. N o w, w e f i nd f ro m t hi s m e m o r -a b l e e x c h a n g e w i t h N E W TO S t h a t b y t 6 7 9 h e h a d m a d e t h e c o r r e c t g u e s s a b o u tt h e f o r m o f th e o r b i t r e s u l t i n g f r o m t h i s l a w.

M o r e t h a n a g u e ss i t c o u l d n o t b e , f o r H OO KE t o t a l l y l a c k e d t h e m a t h e m a t i c a lp o w e r s n e e d e d f o r t a c k l i n g s u c h a p r o b l e m ; o n e m a y e v e n s a y ( as NEW TO N l a t e rac t ua l ly d id , in a f i t o f ange r 37) th a t i t wa s a n ea sy guess , s ince a f t e r a l l i t wa s

33 NEWTON S ann oy anc e is v ividly co nve yed by his la ter acc ou nt of th is corre-spo nde nce with HOOKE to HALLEY (letters nos. 286 an d 288 [2]). H is second reply to -HOOKE is the le t ter no. 238 [2] . I t must be observed that the f igure belonging to th is

• le t ter i s incorrect ly reprodu ced in theCorrespondence; a pho tograp h o f the o r ig inalf igure is g iven in the paper [18] by LOI~N~, in which the present con trov ersy betwee nHo oKE and NEWTON is discussed in gr eat detail .

34 .L ett er no. 239 [2].

35 All re levan t doc um ents abo ut HOOKE S s tudies o n gr avi ta t io n m ay be fo undin LOHXE S excellent pap er [18] In this paper, LOHNE takes HOOKE S side with asmuch a rdour as i f the two con tend ing wor th ies were s t i l l a l ive [ Even though I amnot able to accept a l l h is arguments or to subscr ibe to a l l h is conclusions , I der ivedmuch help f rom his careful analysis .

36 In lette r no. 239 [2].37 In the pas sion ate po stscr ipt of the letter to HALLEY no. 28 8 [21 .



376 L. R O S E N F E L :

kno wn s ince KEP LER'S- t ime tha t . e l l ip tic o rb i t s f i t t ed the obse rva t io ns sa t i s -f ac to ri l y. B u t t o h av e c l ea r ly r e co gn ized t ha t t he shap e o f t he o rb i t is de t e rm ined

' by an a t t r a c t i v e f o r c e f r o m t h e su n obey ing a g iven l aw o f dependence on t hed i s t a n c e , a n d t h a t t h e f u n d a m e n t a l p r o b l e m o f a s t r o n o m y w a s t h e m a t h e m a t i c a lde r i va t i on o f t h e o rb i t f r o m th e l aw o f a t t r a c t i on , r ep r e sen t ed a r emarka b l ein te l lec tua l fea t which i s en t i re ly to HOOKE'S c red i t . EvenNEWTON h o w e v e rgua rde d ly h e b eh a ve d t o w a r ds h i m; i s c and id enough t o a cknowledge 38 t he s t imu-l a t i on he re ce i ve d f ro m H OO KE : Yo ur a cu t e l e t t e r hav in g pu t m e upon cons ide r-i ng t hus f a r t h e s p ec i es o f t h i s c u r ve , I m ig h t add some th ing abo u t i t s de sc r i p t ionb y p o i nt s quam proxime.

This l as t gen tence revea ls a t the sam e t im e th a t NEWTON was SO wel l p re par edto tack le the prob lem tha t in response to HOOKE'S cha l lenge he could rap id ly

m as t e r i t , a t l ea s t in i t s essen t ia l fea tures . As he expla ins e l sewhere in the samele t t e r, h e co n s id e r s mo t i o n a cc o r d in g t o t he .m e th od o f i nd iv i s ib l e s , a s a suc -ce ss ion o f i n n u me r a b l e a n d i n f i n it e l y l i t tl e mo t ions .. . con t i nua l l y gene ra t ed b yg ra v i t y ; a nd t h i s l e ads h i m t o a cons t ruc t i on o f t he t r a j e c to ry po in t b y po in t .I f NEWTON here re fe rs to th e m eth od of ind iv i sib les , i t i s no d ou bt because he d idn o t t h i n k t h a t : H o o K E c o u ld b e a c q u a i n t e d w i t h h is o w n m e t h o d o f f lu x io n s, o fwh ich no th in g w as t he n pu b l i sh ed . To a r r i ve a t a g loba l cha r ac t e r i z a t i on o f t het r a j ec t o ry i s o f c o u r se a m uc h t o u g he r p rob l em , whose gene ra l so lu t ion was r e se rvedto the Le ibn iz ian school . Ho wev er, whe n NEWTON himse l f te l l s us in l a te r me mo r-anda 3° t ha t h e d i d d e du c e t h e e l l i p ti c f o rm o f t he o rb i t f r om the i nve r se squa re

l aw towards t he en d o f t he yea r t 6 79 , we may we l l t r u s t h im to have so lved t h i spa r t i cu l a r c a s e by t h e i n ve rs e me tho d o f f l ux ions even i n i t s r ud im en t a ryform.

A , touc h o f c om e d y i s a d d ed t o t h i s d r am a t i c deve lopm en t by NEWTON'Sacquiescence to I-IOOKE'S e r roneou s s ta t em en t abo ut th e so u the rn dev i a t ion of thefa l l ing body40 . I t i s cur ious th a t NEWTON did n o t no t ice th e e r ror and pers i s tedin i t un t i l h e t o o k up t h e w ho le p rob l em o f t he fo rm o f t he e a r t h wh en wr i t i ng t hePrincipia.

Dur ing t he mo n t h o f N ov em ber t 680 , a spec t acu l a r come t was obse rvedmov ing t ow a rd s t he s un , a nd an o t h e r one was s een i n t he l a t t e r pa r t o f Dec emb erand i n t he f o ll owin g J a n u a r y m oy i ng awa y f rom the sun in t he oppos i t e d i rec t i onwi th abou t t he s a me ve lo c i t y. Th i s p romp ted FLA~STEED, t he r ecen t l y appo in t edAs t ron ome r Ro ya l , t O p u t f o r w a rd t he v i ew ~ t ha t t he tw o come t s we re ac tua l l yone and the s a m e , wh ose pa th h a d unde rgone a comp le t e r eve r s a l i n t he v i c in i t yo f t h e s u n H e e n d e a v o u r e d t o a c c o u n t f o r t h i s e ff e ct b y s o m e m a g n e t i c a c t io no f t he sun , c ha n g in g f r om a t t r a c t i on t o r epu ls i on a s t he co me t en t e r ed t he su n ' s

3s Le tte r no. 238 [2: (last parag raph ).~s These a re qu ot ed in LOHI~E'S pap er[18]. Nevertheless the la t ter contends, in

m y opinion on insuffic ient grounds, th at NEWTON was no t able to solve the prob lem;he repeats this asser t ion in another interest ing paper[22] on NEWTON'S the ory ofcolours.

40 Th e natu re of the erro r is ve ry well expla ined b y LOHNE[18].4x FLA~ISTEED'Sviews_may be inferred from the surv~ving par t of his correspond-

ence on this top ic wi th HALLEY (letter no. 250 [2]) and NEWTON (letters nos. 251 an d254 [2]).



NEWTON. an d' th e L~/w of Gr av ita tio n 377

vor t ex and was t hus de f l ec t ed f rom i ts d i r ec t pa t h t owards t he sun ; he na ive lyimag ined th a t t he m agne t i c ax i s o f t he co me t w ou ld fo llow the de f l ex ion of t he

t r a j ec to ry, so t ha t i t wou ld even tu a l ly p re sen t i t s o the r po le to t he sun : j u s t a sa bul le t, as 'gunners appa ren t ly be l ieved , a lways kep t th e ' sa m e s ide forwa rdalong i ts path. Sol ici ted for his opinion, NEWTON gave a civil , bu t de va stat ingreply~L I t would be tem pt in g to dwel l on i t s re fu ta t ion of FLAMSTEED'S mag net ichypoth es is , s ince i t shows us NEWTON at h i s bes t as a na tura l ph i losopher ; bu ti t is a s ide issue. I shal l only s tress one po int , becau se of i ts intere st for the socialaspec t of the evolu t ion of sc ience : on the opin ion jus t recorded abo ut the beh av-iour of a bu l le t, NEWTON com me nted tha t i t m ay be a t rad i t io n of the gunners ,bu t I do not see how i t can consis t wi th th e laws of mot io n , and therefore dareven tu re t o s ay tha t upon a f a ir tr im i t w il l no t succeed excep t ing some t imes by

acc iden t . Such an u t t e r ance marks t he po in t a t wh ich th e s c ience o f mechan ic seman cipa tes i t se l f f rom the em pir ic ism of c raf t sm en an d en ough conf idence i sf e l t i n i ts l aws to ma ke p red i c ti ons abou t t he ou t come o f ye t un t r i ed expe r imen t s .More to our p oin t , how ever, i s NEWTON'S ex t rao rd i na ry a t t i tud e toFLAMSTEED S

ident i f ica t ion of the two come ts : he i s 'm os t re luc tan t to accept i t 43, because i twou ld make th i s come t pa rad ox ica l ; a ll come t s known so f a r have been obse rvedto mo ve in the same sense On bo th s ides of the per ihe l ion in a line a lmost s t ra ight .No t un t i l t 685 , When he was work ing ou t t he t heo ry o f come ta ry o rb i t s fo r t hePrincipia did he recognize t t ie cor rectness of FLAMSTEED'S ski lful inte rp ret at io nof the observa t ion s ~ .

Never the less , he i s wi l ling to d iscuss th e poss ib i l i ty of a curve d o rb i t and ex~plains 45 to FLAMSTEED th at no repulsive force is need ed to brin g i t ab ou t: ana t t r ac t i on f rom the sun , such as t ha t whe reby the p lane t s ar e kep t i n t he i rcou r se s abou t h im , cou ld p roduce such an o rb i t. On ly t he com e t wou ld then tu rnarou nd the sun , and not (as FLAMSTEED supposed) be def lec ted before reachingi t ; and by a d i r ec t me th od he has o f comp u t ing an o rb it ( o f wha te ve r shape) f romexact observa t ions , he f inds tha t the las t such observ~t tions ( inc luding some of h isown in Feb ru a ry and M arc h 1681) , when ex t r ap o la t ed backwards , i nd i ca t eDece mb er pos i t ions wel l bey on d the sun . Here the n we wi tness NEWTON in posses-s ion of a l l the the ore t ica l too ls enabl ing h im to ass imi la te co me tary mo t ion toth a t of the p lane ts , bu t Severe ly re f ra in ing f rom tak ing the s tep because he i sno t s a t is f ied t ha t i t is g r an t ed b y the d a t a o f obse rva t ion . Ho weve r conv incedhe m a y h a v e been o f t he un ive r sa l i t y o f t he fo rce of g rav i t a t ion , t he s t r i c t r ul e sof h is na tura l ph i losophy forbade h im to draw rash conclus ions .

NEWTON and FLAMSTEED held each oth er in high estee m; in spi te of al l dis-agreement , the tone of the i r cor respondence i s a model of cour tesy and seren i ty.W h e n h e s t a r t e d w o r k o n t h e Principia a t the end of t684 , NEWTON consul tedFLAMSTEED. on various points of astronomical oL~cr.vat ion4~. Am on g oth er things,he was worr ied about the fac t tha t KEPLER'S de termina t ion of Sa turn ' s orb i t

was no t i n ag reemen t w i th t he t h i rd l aw; he suspec t ed tha t t he d i s c repancy42 Le tte rs nos. 251 an d 254[2]48 L et te r no. 255 [2].44 See NEw ToN's let ter .to FLAMSTEEI) of 19 Se pte m ber 16 85 (no. 28 t [2]).a~ L et te rs nos. 254 an d 255 [2].4a Esp ecial ly le tters nos.274 ~275 276 [~].



378 L. R O S E N F E L D

cou ld be du e to t h e pe r t u r b a t i o n o f t h i s o rb i t a t con junc t i on w i th Jup i t e r, andasked FLAMSTEED wh ether he h ad obse rved d ev ia t ions f rom KEPLER'S tab le s a t .

such con ju nc ti on s , co r r e sp on d i ng t o t he e s t . ima t ed :p e r t u rba t i on . I n h i s r~ .p lyFLAMSTEED expressed surpr i se th a t the two. p la ne t s cou ld b e th ou gh t to in f luenceeach o the r t o a n y a p p re c i a b l e am o un t , and gave NEWTON ind i ca t ions abo u t h i sown obse rv a t i ons o f t h e i r o r b i ts . The re upo n NEWTON •exp l ained t ha t i n co mp u t -

• i ng t he pe r t u r ba t i o n o f S a t u r n ' s o rb i t, h e had a s su med an i nve r se squa re ' l aw• o f i n t e r ac t i o n b e t w e e n t h e two p l a ne t s ; b u t he cou ld s ee f rom the new da t a t ha t

h e h a d o v e r e s t i m a t e d t h e " v i r t u e " o f J u p i t e r. " Yo u r i n f o r m a t i o n , " he a d ds ," ab ou t t he e r ro r o f KEPL ER 'S t ab l e s fo r Jup i t e r and Sa tu rn ha s e a sed me O seve ra ls c rup l e s . I wa s a p t t o su s pe c t t h e r e m igh t be some cause o r o the r unknown tome , wh ich m i g h t d i s t u rb t he s e squ i a l t e r a t e p rop o r t i on " (by wh ich is me an t

KEPLER'S th i rd law) . At th i s l a te da te , as we lea rn f ro m th i s inc iden t , h e i s no tye t su r e w h e t he r t h e t h i r d l aw " f i l l s t he heavens" , he s t i l l k eeps an open mindwi th r ega rd t o it s u n i v e r s a v a l i d i t y and s t il l con t emp la t e s t he pos s ib i l it y o f someo the r " caus e" be s id e s g r a v i t a t i o n i n f l uenc ing t he p l ane t a ry mo t ions .

We are now com ing to the las t ac t o f the dr am a. In• sp i te o f h i s renew ed in te r- •e s t i n t he p ro b l em o f g r a v i t a t i on , t he r e i s no s ay ing how long NEWTON wou ldhave gone on w i thh o ld ing p ub l i c a t i on o f h i s power fu l me thod s a nd t he m om en to usconc lu s ions he ha d a l r e ad y r e ach ed w i th t he i r he lp , had i t no t been fo r ano the rfo r t una t e c i r cu ms t an ce w h i ch b ro t l gh t i n to t he p i c tu r e one o f t he mo s t g i ft ed menof the new ge nera t ion , EDMOND HALLEY. Grow n up in the mid s t o f those who hadf i rs t shaken o ff t h e Sh ac k le s of t r ad i t i on and shaped t he mod e rn sp i ri t o f en t e r -p r i se and e nq u i r y, he wa s f o l lowi n g t he i r l e ad w i th a l l t h e e age rness . o f you th andthe v igou r o f a n un c o m m o n i n te l li gence . Adm i t t ed t o t he Roy a l Soc i e ty i n 1678,a t t he age o f t w e n t y - tw o ~ h e w a s a l e r t t o t he ques t ions o f t he day and d i s cus sedthem wi th t he mo s t d i s t i n gu i sh edv i r t u o s i Thus i t h ap pene d 4~ t ha t on one Wed-ne sd ay in Ja n u ar y 1683/4, HALLEY ha vi ng m et Sir CHRISTOPHER WREN an dHOOKEi n t own , t he c o n ve r s a t i o n t u r n ed a s so o f t en be fo r e on t he g r ea t p rob l em o f t hep l a n e t a r y m o ti o n s . H o w t h e m o t i o n h a d t o b e a n a l y s e d a s i n e rt i al d i s p l a c e m e n tmod i f i ed by a t t r a c t i o n , an d ho w one cou ld conc lude t ha t t he a t t r a c t i on obeyedthe i nve r se sq u a re l aw, w as c om m o n knowledge t o t he t h r ee o f t hem, bu t t hec r u x

o f t he m a t t e r w a s ho w f r om t h i s knowledge t o de r i ve t he fo rm o f t he o rb i t. "HoOKE boas t ed t ha t h e c ou ld do it , bu t t he o the r s we re no t t o be con t en t ed w i thme re asser t ions. Sir CHRISTOPHER offered a pr ize o f a bo ok w ort h 40 shi l l ingsto t he one wh o w ou ld p ro du ce t he so lu t i on w i th in two mon ths : need l e s s t o s ayhe had no t t o i nc u r t h e exp en s e .

HALLEY, h owe ve r, d i d no t l e t t he ma t t e r r e s t . I n t he fo l l owing May 4s, he v i s i t edNEWTON in C amb r idge a nd pu t th e ques t ion to h im . NEWTON rep l ied a t o nce

47 Th e sto ry is told b y HALLEY n h is le tte r to NEWTON no. 289 [2]. NEWTONhimself(letter no. 286 [2] to HALLEY ment ions a conversa t ion he had wi th WREN about the

• proble m of the planetary ' orbi ts as e ar ly as t677, when i t seems th at WREN wasalready acquainted with the inverse square law,

4s Ab ou t th e dates of HALLEY'S visits to NEWTON; there is some un cer tain ty du eto discordant testimonies. The question has been ingeniously discussed by HERIVEL[9], whose conclusions I adopt.



NEWTON and the La w of Grav i ta t ion 379

tha t he ha d s ho w n t h e o r b i t t o b e an el li p se , bu t he cou ld no t imme d ia t e ly re -p roduce t he a rg u m en t . He p r om i sed HALLEY to s end i t, and i ndeed he wa s ha rd

a t w o r k d u r i n g J u n e a n d J u l y d r a f t in g a t r e a t i s O 9De Motu i n wh ich he enun -c ia ted in the t rad i t i ona l s ty le , as a succession of def in i t ions , ax io ms an d pro po-s i ti ons, t he l a w s o f m o t i o n a n d t h e i r ap p l i c a t i on t o t he ca se o f t he i nve r se squa rel aw o f a t t r a c t i o n : t h i s wa s t h e k e rne l o f t he fu tu r ePrincipia, and a l so , moreimm ed ia t e ly, t h e t ex t o f h is Lu c a s i an l e c tu re s f o r t he fo l lowing Michae lmas t e rm .HALLEY p ro ba b l y v i s i t e d h im ag a i n i n Augus t 5°, when he l e a r n t t he goo d newst~l at NEWTO N ha d b ro u g h t t h i s d em ons t r a t i o n t o pe r f ec t ion , and i n Nov em berr ece ived a t l a s t t h e p ro m i s e d p ap e r. HALLEY the r eupo n pa id ano th e r v i s i t ~oNEWTON an d p e r s ua d ed h im tha t he ough t t o wr i t e up a f u ll -s cal e book on t hewhole sub jec t . In o rder to a l low h im the requi red lei sure~while secur ing h i s p r io r i ty,

he p roposed t o h ave t h e t r a c t Demotu p re sen t ed t o t he Roya l Soc i e ty and en t e r edup on t he i r r e g i st e r. Wi t h N EWTON'S consen t , he cou ld m ake t h i s ann oun ceme n ta t t he mee t i n g o f t h e t 0 th De ce m ber, an d abou t t he midd l e o f t he fo ll owingFeb ru a ry, t he c op y de s t i n ed t o t he Soc i e ty was r ece ived an d d u ly r eg i s t e r ed 51.

HALLEY had thus no t on ly proc ured the fe l lows of the Soc ie ty the poss ib i l i tyof acqu a in t in g them se lve s wi t hou t de lay w i th the g i s t o f NEWTON'S ideas , bu t hehad even ma nag ed t o l au nc h t he l a t t e r on t he e l abo ra t i on o f a comp le t e expos i -t ion Of them . NEWTON'S in te res t an d en ergy were now th oro ugh ly a roused , andthe work p ro g re s se d w i t h r e m a rk ab l e speed : on Apr i l 28 , 1686 t he m anu sc r i p tof the f i r s t book of the Principia was presen ted to the Soc ie ty52; the second book

fo l lowed i n t h e a u t u m n o f t h a t y ea r and t he t h i rd i n Apr i l t 687 ; t he f i n ishedw o r k a p p e a r e d a b o u t m i d s u m m e r t 6 8 7 : i t w a s H ALLEY a g a i n w h o h a d a s s u m e dal l the chores , as wel l as the f inanc ia l burd en , o f see ing ~ t th ro ugh the pres s53.How could HALLEY succeed so eas i ly in overcoming NEWTON'S ben t to p ro-c r a s t i na t i on a nd b r i ng in g h im t o such momen tous dec i s i ons ? I t h ink t he answeri s s imple : NEWTON was a m an of ve ry sens i t ive d i spos i t ion , who m us t hav e fe l tve ry l one ly am on g t he B o eo t i a n c r owd o f f el lows and s t uden t s ; no wonde r t h a t hea t once f el l u nd e r t he c h a rm o f a b r i ll i an t and en t e rp r i s ing yo ung m an , t o who m hecou l6 exp l a in h i s t ho ug h t s w i th t h e a s su r ance o f an i n t e l li gen t r e sponse . La t e r, hebeh ave d ~ towards FATIO DE DI3ILLIEI~ wi th fa th er ly k indn ess and so l ic itude ,no do ub t fo r th~ s am e reason 54.

Be fo re h e c o u l d h e l p t h e u nd e r t a k ing t o i fs hap py comple t i on , HALLEY hads t il l to w ea th er a s t o rm which p u t to a severe t es t h i s d ip lom at ic t a len t 55. At the

49 One of the four ex tan t versio ns of this treatise is published in ref. [5], pp. 2 37 --292. The moot problem of ascer ta ining the rela t ion of these manuscr ipts with thetext communicated to the Royal Society is thoroughly t reated by HER'IVEL[ ]:

50 L et te r no. 289 [2].sl NEWTONexpresses than ks for the reg istering in his letter no. 278 [2] of 23 Fe br ua ry

1684/5, in which he declares his intention to finish it (i.e. the~proposed book), afterhe has re turned from a journ ey to Lincolnshire , as soon as I can con ven ient l y .

~ Letter no. 285 [2].~s Le tt er s nos. 300, 303, 304, 306, 309 [2].s* The att i tu de of NEWTON tow ards FATIO DE DUILLIER is revealed b y thei r letters

ne w ly publish ed in the third vo lum e of :NEWTON'SCorrespondence. See my review ofth i s vo lume [23].

5~ The acts of this me mo rab le inciden t are the oft-q uot ed letters nos. 285, 286, 288,289, 29.0, 291 [2].



38 L ROSENFELD

memorab l e m ee t i ng O Ap r i l 2 8 , i 686 when much p r a i s e was be ing l av i shed onNEWTON'S d i scover ies j Hoo.KE was p iq ued no t to h ear an y m ent io n of h i s owncont r ib u t ion s to the prob le m, wh ich indeed , as we have:~seen , were en t i re ly in thesame l i ne a s N E WTON ' S . H e ma y we l l be fo rg iven t he human weaknes s o f g iv ingh i s own ide a s a h ig h e r e s t i ma t i on t h an t hey de se rved and even o f f ancy ing t ha tNEWTON ha d b or row ed f ro m h i m the inv erse square l aw. A t the Coffee-housewhe re t he so c i e ty a d j ou r ned a f t e r t he mee t i ng , he vo i ced h i s c l a ims w i thou tsucce ss , t he o th e r s b e in g o f op i n i on t ha t he ha d on ly h imse l f t o b l ame fo r hav ingt ak en no m ore ca r e to s e cu re a d i s cove ry wh ich he pu t s so much v a lue on . T heinc ident w a s r ep o r t e d t oNEWTON v e r y t a c t f u l l y b y HALLEY bu t l ess so b y o thers .I t i n censed h im so m u c h t h a t he t h r ea t e ned t o supp re s s t he t h i rd boo k o f h i s work ,t ha t w h ich h a d t o t r e a t o f t he a s t r ono mica l app l i c a t i ons o f t he t heo ry. He soon

re l en ted , howe v e r, a f t e r a no t he r ep l s t o la rymas t e rp l eceSSof HALLEY s ,wh lc hsoo thedh im to t he e x t e n t t h a t h e e x p r e s s e d r eg re t f or h i s ou tbu r s t o f ange r, and t ouch ing lydec l a red 5~ t h a t he w ou l d a ck n o w l edge h av ing l e a rned f rom H ooKE th a t t he de -v i a t i on o f a f a l li n g bo d y w o u l d b e so u th - ea s t i n ou r l a ti t udes .

NEWTON'S e xasp e r a t i on w as i n deed ou t o f p ropo r t i on w i th t he ob j ec t i ve f ac t so f the c ~ e : HOOKE'S boas t fu ln ess and reck less p r io r i ty c la ims , a r i s ing f rom af i e ry and u nc r i ti c a l i m a g i n a t i o n , we re we ll - known , an d no bod y t ook t h em m oreser ious ly t h .an could be he lped . NEWTON ha d nev er qu i te fo rg iven HOOKE'Sques t i on ing o f h i s op t ic a l d i sc ov e ri e s, and one unde r s t ands t ha t he migh t f e eli r r i t a ti on a t b e i ng o n c e m o r e t h e ob j ec t o f a f u t il e a ccusa t i on ; bu t i n h i s p r e sen t

pos i t ion he could wel l hav e a fforded to ignore i t , Ins te ad , he fi ll s pass ion a te pag esin defence of the or ig ina l i ty o f h is concept ions , re t rac ing the i r o r ig in to h i s s tude ntday s : p rec ious pages indeed t ha t d i sclose to us , besides de ta i l s no t o therwiseknow n, ho w he h imse l f judg ed th e success ive s tages o f h~s inves t iga t ions . '

I t h i s he r e t h a t w e l e a rn , i n t he f i r s t p l a ce , t he c i r cums t ance men t ioned a tt he beg inn i n g o f t h i s e s s a y, t h a t NEWTON had neve r t h oug h t t he i nve r se squa rel aw to r ema i n v a l i d d own to t h e s u r face o f t he ea r t h , un t i l h e had found t he t heo -rem on the a t t rac t ion of spher ica l shel l s some t ime in t685 , whi le he was wr i t ingup t he f i r s t b ook o f t h e Principia Th i s wou ld s eem to s e t t l e t he ques t i on o f t hef a m o u s d i s c r ep a n c y i n t h e e a r l y c o m p a r i so n o f g r a v i t y a n d a t t r a c t i o n : h e c o u l dno t a s c ri be to t h i s e s t i ma t e mo r e t h an an i nd i ca t i ve va lue , and t he r e was t hus l i t t l epo in t , h e th o u g h t , i n i mp r o v i n g i t by u s ing a be t t e r v a lue o f t he e a r t h ' s r ad iu s ;

he wou ld no t h a ve ex pec t e d t h e e r r o r i n t he va lue he adop t ed t o be so l a rge , andwas r a the r i n c li n e d t o r e g a r d t h e d i s c r ep ancy i n ques t i on a s t he measu re o f ar ea l phys i ca l e f f ec t . O n l y a f t e r d i s cove r ing t he t heo rem on t he a t t r a c t i on o f t hesphe re s wo u l d h e s u s pe c t t h e d i s c r epancy t o be spu r ious and v e r i f y t ha t i t a c tua l l yd isapp ears i f one ado pts PICARD'S va lu e for the ea r th ' s rad ius 58. B y tha t t i me

~e Th is is l et te r no. 289 E2].sT L et te r no. 290 [2].58 In his lette r no. 288 [2] to HALLEY, N~WTON mentio ns, in conn ection wi th h is

messa ge to HUYGENS alluded to abo ve, the ea rly pape r (do cum ent no. I 17 [•]) conta in-ing the computat ions of centr i fugal accelerat ions on which this message was based.How ever, he also s ta tes th at in this pap er the rat io of the accelerat ion of gra vi ty tothe centr i fugal accelerat ion of the moon is calculated (a calculat ion unfo rtunat elynot found in the docum ent as we l~ave i t) and the n adds; casual ly, tho ugh n ot ac-curately enough' : .



NEWTON and the Law of Gr av itat ion 381

howeve r, h e h ad s t a r t ed wr i t i n g t he Principia and t he co r r ec t i on o f t he e r ro rha d there fore no in f luence on h i s dec i s ion to publ i sh th e resu l t s o f h is s tud ies.

I n f a c t, h e h a d b y t h e n s o m a n y p r o o fs t h a t t h e l aw o f g r a v i t a t i o n f il ls t h ehea ven s t ha t t h e p a r t i c u l a r a rg u men t wh ich had f ir s t o r i en t ed h i s t houg h t s t oth i s enqu i ry r e ce d ed i n t o c o m p a ra t i ve i n sign if ic ance . I n t h e t h i rd b ook o f t hePrin-cipia i t is m e r e l y u se d t o sh o w t h a t no o the r a t t r a c t i o n t han t he un ive r s a l g r av i -t a t i on ac t s a t t h e su r f a c e o f t h e ea r t h ; and ano th e r sou rce o f i naccu rac y appe a r s :the non -sphe r ic i ty o f the ea r th , i t se l f a consequence of the combi .ned ac t ion ofg r av i t a t i on a n d ~ o ta t i o n so. We ha v e he r e an exam ple o f a f r equen t occu r rence in t h eh i s to ry of sc ience : the degrad a t ion , as I would ca l l i t, o f heur i s t i c a rgu me ntswh ich , once t h e y h a v e p l ay e d t he i r r o le i n gu id ing t he d i s cove re r t o some t r u tho f w ide r sc o p e, a pp e a r i n a d i m m e r l i gh t when t he y a r e con t e mp la t ed f rom the

h ighe r v i ew po i n t t he y h av e h e l pe d t o r e ach .There i s, howev er, in NEWTON'S rev iew of the c i rcum stances man i fes t ing h i s

ea r l y unde r s t a n d i n g o f t h e i nv e r s e squ a re l aw, a r emark ab l e and , I t h ink , ve ryr evea l i ng f ea tu r e : i t i s t he w a y i n wh ich he adduces s° a s ev idence t he pap e r o f1675 on the ae th er hy pothes i s , fo r which he re fe rs HALLEY to th e reg is te r o f theRoya l Soc i e ty. He i s a b i t em ba r r a s sed by t he f ac t t ha t i n t he sho r t pa s sage ong rav i t a t i on i n s e rt e d t h e r e as a n a f t e r t hou gh t ( it was , ' i n t e r l ined a t t he l a s tmo me n t i n t he o r ig i n a l ma n u sc r i p t ) n o men t ion i s mad e o f t he i nve r se squa rel aw; he is so un e a sy ab o u t t h i s t h a t he r e tu rn s t 'o t he m a t t e r i n a f u r t he r l e t t e r slt o HALLEY, i n w h ich he g i ves t he exp l i c it d e r i va t i on o f t he l aw f rom the hypo -

the s is o f an a e the r s t r e am w h i ch I t r i ed :go fo rm u la t e i n mode rn l anguage ea r li e rin th i s essay. Bu t h i s reason for invokin * tl~ is hypothe s i s i s in te res t ing : he po in t sou t t ha t i t l e a d s t o t he inv e r s e s q ua re law on ly up w ard f rom the su rf ace o f ap l ane t , i.e. i n f re e sp ac e , wh e re t h e ve loc i t y o f t he ae the r s t r e am r ema ins co ns t an t ,b u t n o t d o w n w a r d s , i n si d e t h e b o d y, w h e re th e a e t h e r l os es m o m e n t u m .This i s wh y in the cor respond ence w i th HOOliE abo ut the fa l ling bo dy he wasca r e fu l no t t o a s sume t he v a l i d i t y o f t he i nve r se squa re l aw in s ide t he body - -i n con t r a s t t o HOOKE, t h e b un g l e r , w ho was no t awa re of t h i s l im i t a t ion .

A l thoug h h e d e s c ri be s 6. t h e hyp o the s i s , r a t he r m i s l ead ing ly, a s one o f myguesses which I d id no t re ly on , he o bvio us ly regards i t a s suffic ien t to es tab l i sh

the l im i t a t i on i n q ue s t i o n - - o th e rw i se t he r e wou ld be no po in t i n i nvok ing i t t oexpose HOOKE S e r r o r . P e o p l e w h o w a n t t o l o o k u p o nNEWTON a s t he g r ea tma s t e r o f t h e i n du c t i ve me t h od ( wh ich he i s) may be su rp ri s ed , bu t t he r e i t is :habemus con/itentem reum.T he ha l f -hea r t ed admis s ion t ha t he shou ld no t r e l y on

a mere h ypot hes i s whi le he is in fac t re ly ing on i t r evea l s a t ens ion be twee n twotendenc ies equa l ly pow erfu l in NEWTON'S mind , o f which m a n y ins tances can befoun d in h i s wr i t ings. T here w as a con t rad ic t ion be twe en t he r igorous requi re -men t s o f r a t ion a l an a l y s i s an d t he u rge fo r a comprehens ive , i n tu i t i ve syn the s is ,

59 I t is with this complicat ion in mind th atNEWTON, in his letter no. 290 [2].toHALLEY, re tu rn ing to the ear ly paper ment ioned in the preced ing no te , says tha tthe calculat ion of the centr i fugal force ar ising from the ear th 's rotat io n is a thing offar greater diff icul ty than I was aware of . See fur therPrincipia E16~ book I I I , p ro-posi t ion IV.

60 In the le t ter no. 288 [2J , bot h in the bod y of the le t ter an d in the postscr ipt .sx In the let ter no. 290 [2].62 Le tte r no. 288 [2], at the end of the po stscript.

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382 L. R O S E N F E L D

tha t NEWTON could never overcome, and whose roots mu st be sought m uchdeepe r t han in any ques t ion o f sc i en t if ic me thod . Indeed , t he p ro found m ean ingof NEWTON'S concept ion of the ae ther, and the expla na t ion of the ex t rao rd in aryvalue he a t tach ed to i t in a l l h i s l ife can o nly be apprec ia ted aga ins t the genera lphi losophica l and re l ig ious background of h is ac t iv i ty.

Of pa ra m ou nt inf luence on NEWTON'S philosophical out loo k was HENR'~MOREs3' who with BARROW repr esen ted at Camb ridge, i ll NEWTON'S stud ent days,the progress ive cur ren t , open to the modern sp i r i t in sc ience and phi losophy.Both men came f rom the same d is t r ic t o f Lincolnshi re , a Pur i tan s t ronghold ,and i t was a pupi l o f MOR~ who tau ght NEWTON ma them at ics a t Gra nth am school.At Cam bridge th ey rem aine d Close fr iends unt i l MORE'S de ath in t687. MORE

brough t t o Eng land the i deas o f t he I t a l i an human i s t s o f t he X VI th cen tu ry,wh o we re f ight ing the scholast ics by play ing u p PLATO against ARISTOTLE:• hence he becam e kno wn as the "C amb r idge p la tonis t" . This is a misnom er,

however, for l i tt l e of PLATO'S idea l wor ld remains v isib le und er the s t rong pu r i ta ncolour ing MORE appl ied to i t. Indeed , of the two ke y concepts of h is sys tem,space and God, the f i r s t i s der ived f rom the I ta l ian school , the second dec idedlyBr i t i sh . The I ta l ians under the inf luence of the Copern ican v iew of the wor ldma de space inf in ite and conce ived the s ta rs as so man y sys tem s s imi la r to oursf r ee ly roaming th rou gh i t ; t hus space a s the subs t r a tum o f mov ing th ings wasthoug h t o f as ex i s t ing independ en t ly o f t hem and i t s e l f e t e rna l ly a t r e s t. A l l

th ings were conce ived as an imated , wh ether m ater ia l o r immater ia l , m oving inth is subs tan t ia l space , in which God a lso was eve ryw here present . Al l th i s cos-molo gy was tak en over b y MORE, and thro ugh h im by NEWTON as well .

Cha racter is t ic fo r the Eng lish aspe ct of MORE'S syst em is his concep tion ofGod as the absolu te m as ter of the wo r ld , c rea t ing th ings a t wi ll and capab le ofac t ing upon them, o r even des t roy ing them, a t any t ime acco rd ing to h i s owndesigns . In par t icu lar, man ' s re la t ion to God i s tha t of a se rvant to h is mas ter :i t is governed bTf God 's absolu te power, no t b y any of i t s o ther a t t r ibu tes : asNEWTON rem ark s s4, w e say m y G o d " , " m y m a s t e r " , b u t n o t " m y i n f i n i t e " ," m y et ern al" . Yet , God 's omn: .potence is com patib le with ma n's free will , as

wel l as wi th the regu la t ion of a l l na tu ra l phe nom ena b y the laws he has des igned .This ins i s tence on the personal aspec t of God as the ru le r of the wor ld i s a s t r ik ingfea tu re o f r e li gious t hough t i n Eng land in t he l a t t e r pa r t o f t he X VI I th cen tu ry,and i t s h i stor ica l orig in is no t fa r to seek: i t i s indeed a fa i thfu l t ranspos i t ion ontothe theologica l p lane of the pol i tica l ideology developed b y the bourgeoisie a f te rthe fa i lure of i t s f i r s t exper iment in se l f -government and the reca l l o f the k ing .Incapable of f ind ing a source of suff ic ien t au thor i ty among themselves , theyput a l l au thor i ty in the hands of a ru le r no t be longing to the i r own c lass , bu thedged the k ing ' s au thor i ty by law in order to preserve the i r ind iv idua l l iber ty.

- 63 This poi nt is mo st forcefully made in an im po rtan t pap er by M. FIERZ E24~,which also contains a d etailed expo sition of MORE'S ideas an d of their origin in Italianphilosophy.

~4 In th e scholium generale at the end of the second edi t ion of the Principia.This e dition ap peared in 17t 3, bu t NEWTO~r was wo rking on it long b efore; there is adraft of the scholium dating probably from before t697 (about which see ref. [25]and'BREwSTER [13], vo1. 2, p. 154).



NEWTON and the La w of Gr avi tatio n 383

Thus t he su b j ec t sub m i t t ed t o t h e k ing ' s w i l l , bu t expec t ed t he l a t t e r t o a c tacco rd ing t o l a w s d e s i gn ed fo r t h e com mon good and gua ran t ee in g t he f r e edom

of the ind iv idua l .Th i s i s n o t a f a r - f e t c he d t h eo r e t i c a l i n t e rp r e t a t i on . We have d i r ec t ev idencetha t NEWTON'S po l i t i ca l ph i lo soph y was prec i se ly wha t I ha ve ju s t ou t l ined .Wh en K ing JAME S i n F e b r u a r y t 686 /7 t r i ed t o f o rce t he U n ive r s i t y t o adm i t anunqua l i f i ed m on k to the degree of mas te r o f a r ts , NEWTON advised res i s tance 65,no t in a rebe ll ious sp i r i t , bu t because i t was a c lea r l ega li s t ic i s sue : a l l hones tmen a r e ob l ige d b y t h e l aws o f G o d and m an t o ob ey t he k ing ' s lawfu l commands .Bu t i f h is M a j e s t y b e a d v i s e d t o r equ ir e a ma t t e r wh ich canno t be done by l aw,no man ca n su ff er f o r n e g l e c t o f i t . And he con f iden t l y conc ludes : An hones tcourage in these mat te rs wi l l secure a l l , hav ing law on our s ides .

I f the ba lance of po l i t i ca l re la t ions be tw een th e k in g and h i s sub jec t s wasprecar ious , dea l ings wi th the d iv ine power could a l so be t roublesome. Espec ia l lythe p ioneers o f mo der n sc ience , the n a tur a l p h i losophers , were dang erous ly ex-posed to the a l lu re men ts o f mate r ia l i sm, an d had a d i fficu l t course to s tee r b e-tween t h is C h a r y b d i s a nd t he S cy l l a o f pan th e i sm o r de i sm . Aga in s t t he l a t t e r,NEWTON is ca re fu l to w arn u s : God i s no t dura t ion or space , he is ev er l as t in gand eve ryw he r e p r e s en t ; h e i s n o t t he wor ld - sou l , bu t t he wor ld - ru l e r. The ma ina rgum en t f o r u p ho l d i ng t h e c on c ep t i on o f a pe rsona l God was t he o ld one o fde s ign : t he r eg u la r i ti e s of t h e na tu r a l p heno men a could no t have been p rodu cedby chance, t h e y b e t r a y ed t he e x i s t ence o f a sup reme ly w ise and i n t e ll i gen t

be ing who h a d d e s i gn ed e v e r y t h i ng acco rd ing t o t he func t i on i t h a d t o f u lf il i nt he g r and h a r m o n y o f t h e w h o l e cr ea ti on . A t a t ime when t he wonde r s o f na tu r ewere j u s t b e g i n n i n g t o r e ve a l th e m se lve s t o c r it i ca l s c ru t iny, t h i s a rgu men t c a r r i eda grea t weig h t : fo r HUYGENS, i t was ind eed the on ly reason to re ta in a be l ie f ina d e i ty ~6. To the gene ra t ion fo l lowing th a t o f NEWTON, i t was a l rea dy los ing i t sg l amour, an d a t h e i s m b ec a m e t h e f a sh ion. BOYLE was so a l a rme d a t t h i s de t e r i o -r a t i on o f m ora l i t y t ha t h e i n s t i t u t e d by beques t a nnua l l e c tu r e s on t he ev idencesof Chr i s t i an i ty. The f i r s t Boyle l ec tures were de l ivered in t692 by BENTLEY,who i n pa r t i cu l a r a dd uce d a s e v i dence o f de s ign t he cons t i t u t i on o f t he so l a rsy s t em, n ew l y r e du ced t o l aw by NEWTON : he o b t a ined t he l a t t e r ' s a c t i ve supp o r tin ge t t in g h i s a rg um en ts s t ra igh t , and the BENTLEY le t te r s 6~ i l lus t ra te the cur iousmi x tu re o f cau t ion and assurance wi t h which NEWTON hand led f ina l is t i c causa l i ty.

God ha s no t l a i d b a r e h i s d e s i gn t o man , bu t he ha s endowed h im wi th r ea sonso as to e nab le h im to d i scover i t . T he grea t goa l o f NEWTON'S l ife was to d i scoverGod ' s des i g n ~ , b y s t u d y i n g h is w o rks and fo ll owing t he c lue s he had g iven man -k ind th ro ugh h i s p rophe ts . This mo t iv a t i on th row s l igh t on NEWTON'S whole ac -t i v i t y and g iv e s i t u n i t y a n d c o n s is t ency. I t i s a t t he roo t o f h i s choi ce o f me th od :on ly by r a t i o n a l a n a l y s i s o f t h e n a tu r a l phen om ena and r a t i on a l i n t e rp r e t a t i onof the sc r ip tures can we hope to read God ' s message ' , s ince reason i s the too l he

~5 Le tte r no. 301 [2]. Similar views were aga in expressed b y NEWTON on an oth eroccasion two years later: see the letter no. 328 [3].

** Re f. [26] especially p. 524--52 8 and more parti cula rly p. 363 (§ 42).6~ Let te rs nos. 398, 399, 403, 406 ~3].68 NEw Ton 's preoccupat ion w ith the rela t ion of nature and God is a l ready appar ent

in the s tude nt 's essay already quoted abo ut th e Cartesian system (published in ref . ES],p. 89 --156). MORE'S influence is very noticeab le in this essay.

26*



384 L. ROSENFELD

has g iven us for th is purpose . I t expla ins h is li fe -long endeav ours in search of themean ing h idden in the sacred books (which he t rea ted as a ra t iona l problem of

de-coding) and h is e rudi te and pa ins tak ing h is tor ica l inves t iga t ions , which a imeda t e s t ab l ish ing the g rea t an t iqu i ty o f t he Hebrew peop le and the au the n t i c i t y o fthe prophecieseg. Fo r him ther e was no essent ial difference, e i th er in purp oseor in method, be tween the der iva t ion of the laws of na ture f rom the ana lys is ofthe phenomena and the a sce r t a in ing o f God ' s i n t en t ions abou t man ' s f a t e by ar econs t ruc t ion o f t he h i s to ry o f mank ind .

We a re now be t t e r p r epa red to j udge the r ea l p l ace t ha t t he ae the r hypo-thesis o ccup ied in NEWTON'S min d. In the phi lo soph y of MORE and NEWTON,space was occupied by God as wel l as by the c re a ted th ings : b u t how did Godperce ive the th ings an d how could , he ac t up on the m ? A d i rec t in te rac t io n of

God and gross m at te r was out of the ques t ion : God has no sense organs and i sno t a f f ec ted by the mo t ions o f t he bod ie s ; t he l a t t e r do no t expe r ience anyres i s tance f rom God 's omnipresence7° . But could there not be a f iner k ind ofsubs tance provid ing the miss ing l ink ? MORE, as we kno w f rom his fam ous con=t r o v e r s y w i t h DESCARTES had con temp la t ed such a so lu tion , bu t sh runk f rom i tbecause of i t s mater ia l i s t ic f lavour : he was in consequence dr iven to a myst ica lconcep t ion o f sp i r i t s emana t ing f rom God and an ima t ing the c r ea t ed th ings .Myst ic i sm, however, was whol ly av erse to NEWTON'S ra t iona l i s t ic tu rn of mind ,Cartesianism m uc h less so. An aeth erea l f luid f i l ling al l space cou ld, as . DES-CARTES wan ted i t , t ransm i t var ious fo rces be twe en the bodies by appro pr ia te

cyc li c mo t ions : fo r na tu r e , s aysNEWTON71 is a pe rpe tua l c i r cu l a to ry worke r :I t could a lso be the agent of t ransmiss ion of the sensa t ions f rom th e sense organsto the s enso r ium , i n wh ich - - a cco rd ing to t he rud ime n ta ry phys io logy o f t het ime - - these sense impress ions were d i rec t ly perce ived by th e sens ib le subs ta nceof the an imal . L ikewise , by a bo ld an a logyv2, space w ould be as God 's sensorium ,in wh ich he wou ld pe rce ive t he ae the rea l mo t ions and th roug h th em ( if such wa shis wil l ) inf luence those of the material bodies .

I f the ae the r hy pothes is p la yed such a cen t ra l pa r t in NEWTON'S v iew of thewor ld , why d id he not publ i sh i t in the f i r st ed i t ion of thePrincipia ? W h y a tl eas t d id he no t p r e sen t h i s t en t a t i ve t heo ry o f t h e cause o f g rav i ta t i on , w h ichwould have spared h im the imp uta t io n of in t roducin g ac t ion a t a d i s tance as ap r ima ry qua l i t y o f ma t t e r ? By a c rue l i r ony o f fa t e , t he p roo f o f t he un ive r sa lva l id i ty of the inverse square law of gravi ta t ion , h i s grea tes t t r ium ph, had dea l t .asevere b low to h is whole ae therea l con s t ruc t ion . He had a l l the t ime. imagined thece les t ia l bodies mov ing in the ae therea l mediu m would enco unter some res i s tancef rom the l a t t e r, a nd acco rd ing ly expec t ed the i nve rse squa re l aw to be o n lyapprox ima te . Now, t he p l ane t s and the come t s were found to move th rough theheavens in a l l d i rec t ions wi thout revea l ing the leas t p resence of any res i s t ing med i -um. Fro m his own s tudies of the m ot ion of bodies throug h f lu ids, which form the

68 See espec ially refs. Ell] and [12].70 See the scholium generale.71 L et te r no. 146 [1~.7~ Abo ut th e analogy of space as God's sensorium, see especially the que ry 3t a t

the end of the opticks E277,and the contr ove rsy betw een LEIBNIZ and CLARKE (thelatter acting as NEWTON'S spokesm an); th e docu men ts relating to this con trov ersyI~ave been edited with outsta ndin g accu racy b y A. ROBINET~281



NEWTON and the Law o f Gra v i t a t i on 385

s e c o n d b o o k o f t h ePr inc ip ia , N E W TO N w a s f o r c e d t o c o n c l u d e t h a t t h e d e n s i t yo f t h e a e t h e r o u g h t t o b e e x t r e m e l y s m a l l : a n d h o w c o u l d i t th e n f ul fi l t h e r o l e

f o r w h i c h i t w a s p r i m a r i l y c o n c e i v e d ? C o n f r o n t e d w i t h t h i s d i f f i c u l ty, N E W TONd i d n o t r e l in q u i s h e n t i r e l y h i s c o n c e p t i o n o f t h e a e t h e r, b u t h e h a d t o r e s t r i c t i t ss c o p e c o n s i d e r a b l y, c o n f i n i n g i t s a c t i o n s e s s e n t i a l l y t o t h e i n s i d e a n d i m m e d i a t ev i c i n i t y o f t h e m a t e r i a l b o d i e s ; a n d t h e c o n f i d e n t a s s u r a n c e o f t h e e a r l y d a y sw a s g o n e 73. W h e n , m a n y y e a r s l a t e r , a s a n o l d m a n , h e d e c i d e d a t l a s t t o p u b l i s hh i s s p e c u l a t i o n s a b o u t t h e a e t h e r, t o g e t h e r w i t h h i s u n f i n i s h e d o p t i c a l s t u d i e s ,t h e q u e r i es in w h i c h h e p r o p o u n d e d t h e m h a d t h e p a t h e t i c ri n g of r e n o u n c e m e n t .T h e r e i s a n u n d e r t o n e o f r e n o u n c e m e n t a ls o i n t h e l a s t p a g e o f t h escholiumgeneralew h i c h c o n c l u d e s t h e s e c o n d e d i t i o n o f t h ePrincipia . T h e a r r o g a n c e o ft h e s e n t e n c e A n d i t is e n o u g h t h a t g r a v i t a t i o n a c t u a l l y e x i s ts a n d a c t s a c c o rd i n g

t o th e l aw s w e h a v e e x p o s e d d o e s n o t c o n ce a l t h e f a c t t h a t t h i s e x p e r i m e n t a lp h i l o s o p h y i s a p o s i t i o n o f r e t r e a t .

N EW TO N f a i le d in h i s d o u b l e q u e s t . H i s h i s t o r i c a l c o n s t r u c t i o n s f a r e d n o b e t t e rt h a n h i s a e t h e r h y p o t h e s i s : t h e y w e r e b a s e d o n c o n j e c t u r a l i d e n t i f i c a t i o n s w h i c he l u d e d a n y p o s s i b il i ty o f c o n c lu s iv e e x a m i n a t i o n . T h e c o m m o n e r r o r o f h is t i m ew a s t o u n d e r e s t i m a t e t h e m a g n i t u d e o f t h e s e p r o b l e m s . T h e s c a le o f t i m e w a sh o p e l e ss l y d i st o r t e d b y t h e u n q u e s t i o n e d a c c e p t a n c e o f t h e b i b l ic a l t ra d i t i o n ;a n d e v e n t h o u g h t h e n a r r o w f r a m e o f t h e m e d i e v a l w o r ld h a d b e e n s h a t t e r e d b yCOPERNICUSt h e t r u e d i m e n s i o n s o f t h e u n i v e r s e w e r e s t il l fa r f r o m b e i n g r e a l iz e d .N EW T ON b e l ie v e d t h a t t h e h i s t o r y o f m a n k i n d h e l d i n t h e f o u r a n c i e n t k i n g d o m s

o f t h e c l a s si c a l a u t h o r s , a n d t h a t t h e c e l e s t ia l m o t i o n s w e r e c o n f i n e d to t h e s o l a rs y s t e m . A n d a f t e r a lo n g li fe o f u n c e a s i n g t o il , w h e n h e h a d u n r a v e l l e d t h e l a w so f t h e s e m o t i o n s , h e f o u n d h i m s e l f o n th e s h o r e o f a n o c e a n o f t r u t h u n d i s -c o v e r e d a n d w r o t e , r e g r e tf u l ly,hypotheses non ]ingo .

ibliography[11 Th e C orresponden ce of S i r I saac N ewton, vo l . t (1661--1675) . Cam br idge:

Cambr idge Un ive r s i t y P re s s 1959 .[21 The Correspo ndence of S i r I saa c N ewton, vo l . 2 (1676--1687) . C am br idge:

Cambr idge Un ive r s i t y P re s s 1960 .

[3] Th e Correspo ndence of S i r I sa ac New ton, vo l . 3 (1688---1694) . Cam br idge:Cambr idge Un ive r s i t y P re s s t 961 .~41 HA LL, A. R., A nn als of Scien ce 13, 62 (1957).[5] HALL, A. R. & M. BOAS HA LL, Un publ i she d sc ien ti f ic pap ers of I saa c New ton.

Cambr idge : Cambr idge Un ive r s i t y P re s s 1962 .[a] HERIVEL , J. w ., Isis $1, 546 (196o).[71 HERIVEL, J . W ., Is is 52, 410 ( t96 t) .[8] HERIVEL, J . W ., R ev ue d 'his to ire de s sciences 15, t05 (1962).[91 HERIVEL J . w . Archives Intern. d'hist, des sciences 13, 63, 67, 71 (1960).

[10] KOYR~, A. , A rchiv es I nte rn. d 'h is t , des sciences 13, 3 (1960).[11] MANUEL, F. E . , I s aac N ewton h i s to ri an . Cam br idge : Cam br idge Un ive r s i t y P re s s

1963.

~3 LOHNE [22] exa gge ra tes the d i ff icu l ty a r i s ing for NEWTON'S ae th er conce pt ionf rom the absence o f r e s i s t ance t o p l ane t a ry mo t ions when he s t a t e s t ha t i t a l so ove r-th rew h i s a l chem ica l cosm ogony and e s sen t i al pa r t s o f h i s t heo ry o f l i gh t and co lou r s :NEWTON did uph old the fu nc t ions o f the ae th er in chem ica l and op t ica l processes ,wh ich on ly i nvo lve sho r t - r ange in t e r ac t ions ; bu t he had to ab ando n the h op e o f acomprehens ive syn thes i s .



[e ]

L. ROSENFELD: NEWTON and the La w of G rav itatio n86

t12] ROSENFELD, L., N at ur e 202, 43 (t964).~13] BREWSTER, D., Mem oirs of the l ife, w rit ings and discoveries of Sir I saa c Ne wto n.

Edi nb urg h : Thom as Constable t 855.

[ 4] THOMSON W. & P. G. TAIT Treat ise on natura l p hi losophy. Cam bridge : Camb ridgeUnivers i ty Press t879.

~15~CAJORI, F. , in: Sir Isa ac Ne wto n 1727--1927, p . 127- - t88 . Ba l t imore : Wi l-liams & Wil kins 1928.

[16] NEWTON, I . , Phf losophiae natural is pr incipia m athe ma t ica . Lon dini : Reg. Soc.1687

[171 STq~KELE¥,W.: Mem oirs of Sir Isa ac N ew ton 's l ife Et752]. Lo nd on : Ta ylo r &Fr an ci s t 936.. .

[18] LOHNE, J., Ce nt au ru s 7, 6 (1960).E19J GALILEI, G., Dialogo dei due m assimi sistemi de1 mo ndo . F irenz e: L and ini i632.

Giornata seconda ( f rom: La ver t ig ine veloce ha facul t~ di es t rudere e dis-sipare ) .

HUYGENS C. Oeuvres completes, tome t6 (L aH ay e : Ni jhoff t929) : De v icentr i fuga ( t659) , p . 237--32 8.

[21] HUYGENS, C.: Horo log ium oscil latorium. Parisi is: M ugu et t673. (Oeuvres com -pletes , tom e 18. La Hay e: N i jhoff t934.)

[22] LOHNE, J . , A rchive for the His tory of Ex ac t Sciences 1 , 389 ( t961) .[23] ROSENFELD, L., Na tu re 19S, 414 (1962).[24] FIERZ, M., G esn eru s 11, 62 (i95 4).[2@ GREGORY, J. C., Tra nsac tions of the Ro ya l Soc. of Edi nb ur gh 12, 64 (1829):[26] HUYGENS, C., Oeuvres comp letes, tom e 21. La H ay e: Nijh off 1944.[27] NEWTON, I. , Opticks, 2nd edition. Lo nd on : W . In ny s t 7t 7.[28] ROm~IET, A., Correspo ndan ce Leibniz-Clarke. Par is: Presses Un iversitaires de

France 1957.

[29] WHITESlDE, D. T., Notes and Rec ords of the Ro ya l So ciety 19, 53 (t964).[3 ] WHITESIDE D. T. Briti sh Jo ur na l fo r Hist. of Science 2, 117 (t 964).

N o r d i t aCopenhagen

(Received April 4, 1965)

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Rosenfeld (1965) Newton and the Law of Gravitation

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